A critical hurdle of a nonlinear vibration system in fractal space is the inefficiency modelling system. Specifically, differential equation models cannot elucidate effect porosity size and distribution periodic property. This paper establishes fractal-differential model for this purpose, Duffing-Van der Pol oscillator (DVdP) with two-scale derivatives forced term considered as an example to re...

Two-point correlation function of galaxy distribution shows that the structure in the present Universe is scale-free up to a certain scale (at least several tens Mpc), which suggests that a fractal structure may exist. If small primordial density fluctuations have a fractal structure, the present fractal-like nonlinear structure below the horizon scale could be naturally explained. We analyze a...

We present comparative results obtained in the context of 24-bit true color image encoding by using searchless vs. search-based fractal compression techniques in a perceptually uniform color space. A pixel in the color space is represented as a vector with each component corresponding to a color channel. The least squares approximation of an image block by an Iterated Function System (IFS) is a...

The formation length of particles produced in the relativistic collisions of hadrons and nuclei has relevance to fundamental principles of physics at small interaction distances. The relation is expressed by a z scaling observed in the differential cross sections for the inclusive reactions at high energies. The scaling variable reflects the length of the elementary particle trajectory in terms...

The attractor is a central object of an iterated function system (IFS), and fractal transformations are the natural maps from the attractor of one IFS to the attractor of another. This paper presents a global point of view, showing how to extend the domain of a fractal transformation from an attractor with non-empty interior to the ambient space. Intimitely related is the extension of addressin...

We introduce fractal liquids by generalizing classical liquids of integer dimensions d = 1, 2, 3 to a fractal dimension df . The particles composing the liquid are fractal objects and their configuration space is also fractal, with the same non-integer dimension. Realizations of our generic model system include microphase separated binary liquids in porous media, and highly branched liquid drop...

Riesz potentials of fractal measures μ in metric spaces and their inverses are introduced . They define self–adjoint operators in the Hilbert space L2(μ) and the former are shown to be compact. In the Euclidean case the corresponding spectral asymptotics are derived with Besov space methods. The inverses of the Riesz potentials are fractal pseudodifferential operators. For the order two operato...